Effect of magnetic field on the natural convection from a vertical melting substrate

This paper presents a self-similar solution of the coupled problem of magneto-hydrodynamic free convection flow of an electrically conducting fluid arising from melting of a semi-infinite solid substrate. At steady state, buoyancy induced free convection of the electrically conducting fluid is influenced by the Lorentz force. A set of governing PDEs is developed for a two dimensional boundary layer problem including phase change which is simplified to a set of ODEs using a similarity transformation and are solved iteratively using an implicit Keller-box method. An asymptotic analytical solution for melting and heat transport rates is also presented for the case of small Prandtl numbers. The effect of each of the three characteristic parameters, viz., the Prandtl number, the melting parameter and the Lykoudis number on the similarity velocity and temperature profiles in the boundary layer over melting substrate is studied. It is observed that increasing the Lykoudis number or decreasing the Prandtl number lowers the melting rate and heat transfer at the substrate–melt interface. The use of magnetic field in controlling the free convection heat transfer, the melting rate and the thickness of the velocity and thermal boundary layers over melting substrate is elucidated and discussed.